Abstract

This study is about the Quality. Here I have dealt with the quality that differs significantly from the common understanding of quality /as determined quality/ that arise from the law of dialectics. This new quality is the quality of the quantity /quality of the quantitative changes/, noticed in philosophy by Plato as “quality of numbers”, and later developed by Hegel as “qualitative quantity. The difference between the known determined quality and qualitative quantity is evident in the exhibit form of these two qualities. The exhibit form of the known determined quality from the law of dialectics /or it transformation/ is related with discreteness and abrupt changes. The exhibit form of the qualitative quantity /and it transformation/ is related with the continuity and gradual transition from one condition, to a different condition, without any abrupt changes. In my paper “Quality of the quantity”, I have argued that one of the most ancient implementation of quality of the number can be found in the dimensional mathematical model of point – line – surface – figure - introduced by Plato. The most whole presentation of the idea of quality of number in Plato is embeded in his teaching about the "eidical number". The quality of the quantity emerges as criteria for recognizing the difference between the eidical numbers and natural arithmetical number. The thesis concerning Plato is based on the The Unwritten Doctrine of Plato and one of the most original works in the history of philosophy written in the 20th century - “Arete bei Platon und Aristoteles” – “Arete in Plato and Aristotle” /Heidelberg 1959/ written by Hans Joachim Krämer. The new quality as the quality of the quantity /quality of the quantitative changes/, first noticed in philosophy by Plato as “quality of numbers” was developed in Hegel as “qualitative quantity”. Hegel proclaimed the Qualitative quantity, or Measure in the both of his Logics -The Science of Logic / the Greater Logic/ and The Lesser Logic/ Part One of the Encyclopedia of Philosophical Sciences: The Logic. In my paper I have offered the arguments that the concept of quality of the quantity should be enhanced with the adopted methodological approach of analogy with an implementation in the field of the Topology - Analysis Situs, developed by the Jules Henri Poincare. In the topology we could see homeomorphism as exhibit form of Quality on the Quantity. The explicit form of the quality of the quantity transformation is the continuous deformation – typically known in topology as homeomorphism. The concept of qualitative quantity is linked with the concept “structural stability” and nonequilibrum phase transition. The concept of structural stability is related with the topological homeomorphism. In his book “Synergetics: Introduction and Advanced Topics” /Springer, ISBN 3-540-40824/, in the Chapter 1.13. Qualitative Changes: General approach, p. 434-435, Hermann Haken explores and illustrate the structural stability with an example /figure 1.13, p.434/ given by of D'Arcy W. Thompson, the Scottish biologist, mathematician and classics scholar and pioneering mathematical biologist, Nobel Laureate in Medicine /1960/, the author of the book, On Growth and Form, /1917/. The quality of the quantity could be seen in the Herman Haken’s citation on the D'Arcy W. Thompson. My thesis is that the topological homeomorphism is the explicit form of the quality of the quantity transformation. The qualitative quantity change which becomes phenomenon, according to Émile Boutroux, is the subject of study in Cultural Phenomenology of Qualitative quantity. Our approach to this subject is Poincaré Model of the Subconscious Mind in Mathematics, which is the most suitable tool to unfold the arhetype of qualitative quantity.